What is the solid angle subtended by the moon at any point of the Earth, given the diameter of the moon is 3474 km and its distance

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What is the solid angle subtended by the moon at any point of the Earth, given the diameter of the moon is 3474 km and its distance from the Earth 3.84 × 108 m?


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Salim Ahmed Kawsar

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Given: Diameter (D) = 3474 km

∴ Radius of moon (R) = 1737 km

= 1.737 × 106 m

Distance from Earth r = 3.84 × 108 m

To find: Solid angle (dΩ)

Formula: dΩ = \(\frac{dA}{r^2}\)

Calculation:

From formula,

dΩ = \(\frac{\pi R^2}{r^2}\) ……..( cross-sectional area of disc of moon = πR2)

dΩ = \(\frac{\pi\times(1.737\times10^5)^2}{(3.84\times10^8)^2}\)

= \(\frac{3.412\times(1.737)^2\times10^{10}}{(3.84)^2\times10^{16}}\)

= antilog{log(3.142) + 2log(1.737) – 2log(3.84)} × 10-6

= antilog {0.4972 + 2(0.2397) – 2(0.5843)} × 10-6

= antilog{0.4972 + 0.4794 – 1.1686} × 10-6

= antilog{\(\overline{1}\) .8080} × 10-6

= 6.428 × 10-1 × 10-6

= 6.43 × 10-5 sr

Solid angle subtended by moon at Earth is 6.43 × 10-5 sr

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